EXCHANGE 


Studies  of  Mental  Fatigue 


In  Relation  to  the  Daily  School  Program 


W.  H.  HECK,  M.  A. 

PROFESSOR  OF  EDUCATION,  UNIVERSITY  OF  VIRGINIA 

AUTHOR  OF 
"MENTAL  DISCIPLINE  AND  EDUCATIONAL  VALUES" 


SUBMITTED  IN  PARTIAL  FULFILMENT  OF  THE  REQUIREMENTS 
FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  COLUMBIA  UNIVERSITY 


LYNCHBURG,  VIRGINIA 

J.  P.  BELL  COMPANY,  INCORPORATED,  PRINTERS 
1914 


LBlc 


TABLE  OF  CONTENTS 

PAGE 

INTRODUCTION    3 

FIRST  STUDY 5 

Conditions    5 

Material    6 

Method    10 

Grading    15 

Kesults    17 

SECOND  STUDY 27 

THIRD  STUDY 33 

CONCLUSIONS 37 


STUDIES  OF  MENTAL  FATIGUE 


INTRODUCTION 

American  books  on  school  management  and  hygiene1  show  a 
practical  though  not  complete  agreement  as  to  the  curves  of 
fatigue  in  relation  to  the  daily  school  program.  Conclusions 
from  German  experiments  on  fatigue  are  the  main  bases  for 
this  American  opinion,  which  is  somewhat  as  follows:  The 
child's  efficiency,  on  the  average,  is  greatest  from  about  9  :30 
(after  a  period  for  settling  down  to  work)  to  11  A.  M.,  and  then 
declines  until  the  noon  intermission;  the  child  comes  back  in 
the  afternoon  partially  refreshed  by  the  long  recess  and  the  mid- 
day meal,  depending  of  course  upon  the  length  of  the  recess 
(usually  one  hour)  and  the  quantity  and  quality  of  the  food 
eaten ;  the  second  high  plateau  of  efficiency,  which  is  lower  than 
the  corresponding  plateau  of  the  morning  session,  extends  from 
about  1 :30  to  2 :30  P.  M.,  and  is  followed  by  a  decline  to  the 
lowest  point  of  the  day  at  the  time  of  dismissal.  Some  writers 
believe  that  the  second  plateau  occurs  later  in  the  afternoon 
than  1 :30  p.  M.  In  a  one-session  school  day  the  decline  from 
the  high  morning  plateau  is  interrupted  to  only  a  small  degree 
by  one  or  two  short  recesses,  and  extends  to  a  point  below  that 
at  the  close  of  the  morning  session  of  a  two-session  day. 

Such  text-book  opinions  are  fast  becoming  guides  for  making 
daily  school  programs  throughout  the  United  States.  Univer- 
sity departments  of  education,  normal  schools,  summer  schools, 
and  teachers'  reading  circles  are  also  urging  reform  in  programs 
according  to  the  following  suggestions:  The  most  difficult  sub- 
jects in  the  curriculum,  if  they  can  be  determined  for  a  particu- 
lar class,  should  be  placed,  both  for  class  recitation  and  for 
individual  study,  at  the  periods  of  greatest  efficiency,  with 
special  emphasis  upon  the  high  morning  plateau  for  arithmetic 

*For  example:  Arnold,  School  and  Class  Management,  Vol.  II,  p.  33; 
Bagley,  Educative  Process,  pp.  340-2,  and  Classroom  Management,  p.  57; 
Bolton,  Principles  of  Education,  pp.  274-5;  Chancellor,  Class  Teaching  and 
Management,  pp.  122,  3;  Colgrove,  The  Teacher  and  the  School,  p.  180; 
Cornell,  Health  and  Medical  Inspection  of  School  Children,  p.  193; 
Hellister,  High  School  Administration,  p.  254;  O'Shea,  Dynamic  Factors 
in  Education,  pp.  286-290;  Perry,  Management  of  a  City  School,  pp.  99, 
100;  Roark,  Economy  in  Education,  pp.  65,  94;  Seeley,  New  School 
Management,  p.  49;  Shaw,  School  Hygiene,  pp.  230,  1. 


4  STUDIES  OF  MENTAL  FATIGUE 

or  language  drill ;  the  less  difficult  subjects  should  be  distributed 
appropriately  along  the  curves  of  fatigue ;  and  recesses,  relaxa- 
tion exercises,  and  alternations  of  recitation  with  study  periods 
should  be  used  to  defer  and  lessen  the  decrease  in  efficiency. 
Thus  the  waste  of  the  child's  energy  would  be  checked  and  more 
school  work  be  accomplished  in  a  given  time. 

The  purpose  of  this  monograph  is  not  to  review  the  vast  and 
bewildering  literature  on  fatigue,  or  even  that  which  has  domi- 
nated American  thought  on  the  daily  school  program,  but  to  re- 
port experiments  testing  the  validity  of  the  prevailing  American 
opinion  and  the  suggestions  based  thereon.1 


*I  am  greatly  indebted  to  Dr.  Edward  L.  Thorndike,  Teachers'  College, 
Columbia  University,  for  many  suggestions  regarding  this  work.  The  sum- 
maries of  experiments  on  Fatigue  in  his  Educational  Psychology,  vol.  iii, 
and  in  Offner's  Mental  Fatigue  (English  translation  by  Whjpple)  render 
unnecessary  any  bibliographical  discussion  in  this  monograph.  My  second 
and  third  experiments  were  reported  in  the  PsycJiological  Clinic  and  the 
Journal  of  Educational  Psychology. 


FIRST  STUDY 

CONDITIONS. 

The  tests  were  given  during  the  session  1911-12  to  forty 
classes,  1,153  children,  in  four  New  York  City  schools,  repre- 
senting different  nationalities  and  different  grades  of  social  and 
hygienic  opportunities.  On  four  days  (each  being  four  or  five 
days  apart)  in  December,  1911,  four  classes  of  fifth-grade  girls, 
mainly  Russian  Jews,  were  tested  in  Public  School  177 ;  on 
four  Fridays  in  January,  1912,  eight  classes  of  5A  boys,  and  on 
four  Mondays  eight  classes  of  5B  boys,  mainly  Italians  and  Pol- 
ish Jews,  were  tested  in  Public  School  83 ;  on  four  Wednesdays 
in  January  four  fourth-grade  and  four  fifth-grade  boys  and 
girls,  mainly  Irish,  German,  and  American,  were  tested  in  Pub- 
lic School  27;  on  two  Wednesdays  in  March  and  two  in  April 
six  fifth-grade  and  six  sixth-grade  boys  and  girls,  mainly  Ameri- 
can (with  several  negroes),  were  tested  in  Public  School  3, 
Brooklyn.  Fifteen  of  the  forty  classes  tested  were  5A  classes 
and  fifteen  were  5B  classes.  Together  they  furnished  the  stand- 
ard for  the  work,  but  two  4A,  two  4B,  three  6A,  and  three  6B 
classes  were  chosen  to  represent  other  stages  of  advancement. 
The  normal-aged  and  over-aged  (E)  sections  of  the  half-grades 
in  P.  S.  177  and  the  high  (a),  middle  (b),  and  low  (c)  sections 
of  the  half-grades  in  P.  S.  3  were  included,  as  were  also  the  un- 
differentiated  sections  in  P.  S.  83  and  27.  Of  course  the  differ- 
ent ability  of  classes  of  different  stages  of  advancement  did  not 
affect  my  results,  because  in  any  comparison  of  the  work  at  the 
four  periods  of  the  school  day  the  work  of  the  same  class  would 
be  represented  at  each  period,  and  thus  would  be  compared  with 
itself  and  not  with  a  less  or  more  advanced  class.  The  tests  in 
P.  S.  177,  83,  and  27  came  before  the  mid-session  promotion; 
those  in  P.  S.  3  came  after,  and  therefore  were  given  to  some- 
what younger  and  less  advanced  children  according  to  grade. 
Though  more  boys  than  girls  took  all  four  of  the  tests,  the  re- 
sults fairly  represent  both  sexes.  The  December,  March,  and 
April  tests  were  given  in  mild  weather,  the  January  tests  in 
cold  weather;  and  the  ventilation  of  the  classrooms  was  corre- 
spondingly varied,  especially  by  the  use  of  window  ventilation. 
The  ventilating  and  lighting  systems  were  excellent  in  P.  S. 
27,  good  in  P.  S.  177,  and  fair  in  P.  S.  83  and  3.  Twenty 
classes  were  tested  on  Wednesdays,  eight  on  Fridays,  eight  on 
Mondays,  and  four  on  different  days  in  the  week,  thus  repre- 
senting supposedly  varied  degrees  of  freshness  in  children  in 
relation  to  the  week's  schooling.  The  children,  tested  were 


6  STUDIES  OF  MENTAL  FATIGUE 

under  medical  supervision  and  their  most  obvious  physical 
defects,  especially  of  a  contagious  kind,  had  been  looked  after ; 
but  very  few  children  had  been  given  a  general  routine  exam- 
ination by  the  school  doctors.  The  daily  school  programs  were 
not  uniform,  sometimes  even  in  the  same  school,  but  showed  a 
general  tendency  to  give  arithmetic  in  the  early  morning.  In 
P.  S.  83  a  group  system  was  used  throughout^  about  half  of  a 
class  being  grouped  around  the  teacher  for  study  while  the 
other  half  carried  out  previous  directions  as  to  work  at  black- 
boards or  desks. 

The  differences  as  to  social  and  hygienic  condition  of  children 
and  schools,  and  as  to  months  and  days,  did  not  affect  my  com- 
parisons of  the  work  of  the  classes  at  four  periods  of  the  school 
day,  because  the  classes  were  tested  and  compared  in  groups 
of  four,  every  class  in  a  group  having  almost  the  same  conditions 
and  being  tested  on  the  same  days.  These  variations  in  the 
groups  as  a  whole  were  purposely  sought  to  see  if  any  conse- 
quent changes  could  be  noticed  in  the  work  of  the  groups  as  com- 
pared with  each  other,  but  they  were  so  slight  as  to  be  negligible. 
The  differences  in  children  and  schools  were  representative 
of  New  York  City  school  conditions,  though  the  four  schools 
selected  were  superior  in  supervision. 

MATERIAL. 

As  my  aim  was  to  find  out  what  decrease  in  efficiency  re- 
sulted from  the  progress  of  the  day  and  especially  of  the  school 
work,  I  determined  to  test  a  large  number  of  children  at  four 
different  periods  of  the  school  day  and  compare  the  quantity 
and  the  quality  of  the  work  done.  Xot  the  slightest  change 
was  to  be  made  in  the  ordinary  school  routine  except  the  in- 
terruptions for  the  short  time  necessary  to  give  the  tests.  My 
desire  was  to  select  test  material  as  nearly  like  the  actual  lessons 
of  the  children  as  possible  and  thus  avoid  the  artificiality,  at 
least  for  my  purpose,  of  most  of  the  physiological  and  psycho- 
logical tests  so  far  made.  I  therefore  chose,  as  most  suitable 
for  my  purpose,  the  four  fundamental  operations  of  addition, 
subtraction,  multiplication,  and  division  with  whole  numbers. 
Of  course  these  operations  could  not  represent  all  of  arithmetic 
or  all  of  the  curriculum,  but  neither  could  any  other  test 
material;  and  as  the  basis  of  all  number  work  they  were  as 
representative  as  any  part  of  the  elementary  curriculum 
could  be. 

In  order  to  carry  out  my  plan  of  testing  children  at  four 
periods  of  the  school  day,  and  comparing  the  work  done,  I  had 


MATERIAL  7 

/to  have  four  different  tests  so  similar  in  quantity  and  quality 
that  a  certain  proportion  of  correct  and  incorrect  work  in  the 
first  test  would  be  as  nearly  equal  as  possible  to  the  same  pro- 
portion in  any  one  of  the  other  three  tests.  Only  in  this  way 
could  the  work  at  the  four  periods  be  conveniently  compared. 
Of  course  it  was  impossible  to  have  four  different  tests  exactly 
equal  as  to  quantity  and  quality,  but  the  reader  can  see  from 
the  third  and  fourth  tests  herein  printed  that  this  result  was 
very  nearly  approached. 

As  the  Standard  Tests  in  Arithmetic,  by  Mr.  S.  A.  Courtis 
of  Detroit,  are  widely  recognized  as  well  planned  and  graded, 
I  obtained  Mr.  Courtis'  kind  permission  to  modify  and  use 
his  Test  No.  7,  and  also  his  imitation  of  it,  which  differed 
almost  entirely  by  a  shifting  of  the  figures  in  each  example. 
With  my  first  and  second  tests  thus  furnished,  I  made  out  the 
third  and  fourth  in  imitation  of  these  by  a  similar  shifting  of 
the  figures.  In  the  few  examples  where  a  figure  was  substituted 
by  Mr.  Courtis  in  the  second  test  for  one  in  the  first,  that 
figure  reappeared  in  the  fourth  test  but  not  in  the  third.  Mr. 
Courtis'  tests  were  not  entirely  suitable  for  my  purpose  in  three 
particulars:  (1)  The  required  transfer  by  the  child  of  the 
examples  and  of  the  answers  could  not  be  reduced  to  a  propor- 
tionate measurement  along  with  the  work  in  the  operations 
themselves.  Consequently  each  example  in  my  tests  was 
printed  in  workable  form  with  space  underneath  for  the  figures 
to  be  made  by  the  child.  (2)  The  arithmetical  symbols  were 
eliminated,  and  the  operations  necessary  were  designated  by 
the  words,  "Add,"  etc.,  above  the  examples.  (3)  Example 
la,  2 a,  9,  and  17  were  omitted,  thus  making  each  test  consist 
of  three  examples  each  in  addition,  subtraction,  multiplication, 
and  division.  The  examples  were  printed  in  three  parallel 
rows,  each  row  with  one  example  in  each  operation  in  the  order 
just  given.  (These  modifications  were  made  by  me  without 
consulting  Mr.  Courtis,  and  he  is  in  no  way  responsible  for 
them.)  The  first  row  contained  examples  with  no,  the  second 
with  simple,  and  the  third  with  advanced,  borrowing  and  carry- 
ing. However  advantageous  it  might  have  seemed  for  all  the 
examples  to  have  been  of  approximately  equal  difficulty,  the 
wisdom  of  Mr.  Courtis'  three  grades  of  difficulty  was  shown 
in  the  zest  gained  by  the  children  in  my  tests  from  the  rapid 
start  with  the  easy  examples  of  the  first  row.  (The  third  and 
fourth  tests  are  herewith  given,  the  original  size — 8%  x  11 
inches — and  type  being  reduced.) 


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10  STUDIES  OF  MENTAL  FATIGUE 

METHOD. 

I  explained  to  the  teachers  beforehand  the  purpose  and 
method  of  my  experiments  and  asked  them  to  remain  in  the 
room  while  the  tests  were  being  given.  They  were  earnestly 
requested  not  to  take  any  part  in  explaining  or  directing  the 
work,  not  to  discuss  the  tests  with  the  children  at  other  times, 
and  not  to  vary  the  prescribed  arithmetic  lessons  in  the  slightest 
so  as  to  stress  the  four  fundamental  operations.  (The  children 
were  doing  more  advanced  work.)  As  far  as  I  know,  these 
requests  were  faithfully  carried  out,  and  the  teachers  were 
always  courteous  in  making  way  for  my  work.  I  eliminated 
the  teachers  from  any  part  in  conducting  the  tests,  because 
uniformity  in  method  was  possible  only  with  one  conductor 
throughout. 

The  presence  of  the  teacher  in  a  classroom  gave  the  customary 
organization  as  a  background  for  my  tests.  The  method  of 
presenting  the  tests  to  the  children  was  worked  out  with  great 
care.  When  I  entered  a  classroom  for  the  first  time,  the  teacher 
directed  the  children  to  put  aside  whatever  work  they  were 
doing  individually  or  collectively.  I  then  explained  the  nature 
of  my  four  tests,  the  order  in  which  the  examples  were  to  be 
done  (with  a  caution  not  to  skip  the  examples  in  division) ,  and 
the  directions  for  starting  and  stopping  work  immediately  on 
signal.  These  explanations  were  almost  the  same  to  all  classes 
and  seemed  so  clear  that  most  of  the  children  began  the  first 
test  with  nearly  as  much  understanding  as  they  did  the  other 
three.  An  inevitable  initial  interest  partly  balanced  whatever 
initial  disadvantage  the  children  may  have  had  in  the  first  test. 
The  introductions  to  the  later  tests  were  very  brief.  The 
children  thought  they  were  being  examined  for  correctness  in 
speed  and  never  realized  the  main  purpose  of  the  tests.  More- 
over, they  did  not  know  that  their  results  would  have  no  effect 
upon  their  school  standing. 

When  all  pencils  were  ready  (in  P.  S.  83  pens  were  used) 
the  teacher  and  I  put  on  each  desk  one  test  sheet  with  the  back 
side  up.  The  children  were  not  allowed  to  touch  the  tests  until 
told  to  write  on  the  back  of  the  sheets  the  number  of  the  school, 
the  date,  and  the  name,  age,  and  class  of  pupil.  (Later  on  I 
inserted  the  time  of  day  when  the  test  began.)  On  signal,  the 
children  turned  the  papers  over  immediately  and  began  to  work 
the  examples  in  the  numbered  order.  They  worked  steadily  as 
directed,  with  surprisingly  little  hurry  or  interruption,  until 


METHOD  11 

told  to  stop,  when  they  turned  their  papers  over  without  put- 
ting down  another  figure.  During  the  test,  I  quietly  watched 
the  children  and  their  papers,  so  as  to  prevent  cheating,  toward 
which  there  was  little  inclination,  and  to  see  that  the  examples 
were  worked  in  proper  order  and  without  hurry,  especially 
toward  the  end.  The  children  did  not  know  how  much  time 
was  being  allowed,  the  progress  of  time  was  not  mentioned,  and 
I  consulted  my  watch  almost  without  being  noticed. 

The  time  limit  for  each  test  was  ten  minutes,  not  long  enough 
for  the  children  to  be  fatigued  by  the  test  itself.  Great  care 
was  taken  to  be  exact  in  starting  and  stopping.  The  first  four 
(those  in  P.  S.  177)  of  the  forty  classes  tested  were  given 
twelve  minutes,  which  time,  of  course,  was  maintained  through- 
out the  four  tests  with  these  classes,  and  did  not  affect  the  total 
results  as  far  as  my  purpose  was  concerned — the  twelve-minute 
tests  being  compared  only  with  each  other.  But  as  many 
children  in  these  four  classes  finished  in  ten  or  eleven  minutes, 
the  time  limit  was  reduced  to  ten  with  the  other  classes.  Even 
then  several  children  finished  a  little  before  ten  minutes  and 
generally  spent  the  extra  time  in  looking  over  and  correcting 
their  work. 

Those  children  that  finished  early  put  themselves  at  a 
possible  disadvantage,  if,  in  their  speed,  they  sacrificed  quality 
to  quantity  and  were  unable  to  increase  the  quantity  further 
by  working  extra  examples  up  to  the  full  time  allowed.  How- 
ever, as  the  total  tests  showed  slightly  more  work  and  a  slightly 
greater  per  cent  of  error  at  the  periods  after  the  first  period, 
these  disadvantages  might  have  had  slightly  more  influence 
and  been  added  to  the  fatigue  effect  at  those  periods.  That 
this  difference  is  small  is  shown  by  the  fact  that  the  five  groups 
which  included  far  more  than  half  of  the  completed  tests  had, 
as  averages  for  the  five  groups  and  for  the  three  periods,  a 
smaller  increase  in  amount  of  0.47  per  cent,  and  only  a  greater 
decrease  in  correct  work  of  0.04  per  cent  than  did  all  the  ten 
groups  combined  into  one  total  group.  If  any  possible  dis- 
advantage affected  the  results  of  these  five  groups,  it  was 
swallowed  up  in  their  superior  ability.  In  a  note  on  page  21 
are  given  the  comparisons  of  the  four  periods,  after  the  results 
of  the  twelve-minute  tests  in  P.  S.  177,  which  many  children 
finished,  were  subtracted  from  the  total  group  with  its  similar 
comparisons.  The  comparisons,  before  and  after  this  subtrac- 
tion, are  so  nearly  alike  and  the  slight  differences  are  so  con- 


12  STUDIES  OF  MENTAL  FATIGUE 

flicting,  as  signs  of  fatigue,  that  it  matters  little  whether  the 
differences  be  attributed  to  early  finishing  or  to  chance  varia- 
tion in  P.  S.  177.  Whatever  small  effect  early  finishing  in 
the  ten  groups  tested  may  have  had  upon  my  results,  this  effect 
would  strengthen  my  conclusions  as  to  the  little  fatigue  shown 
in  my  tests,  because  the  subtraction  of  it  from  the  fatigue 
effect  would  lessen,  of  course,  the  signs  of  fatigue  just  to  that 
degree.  In  fact,  I  might  emphasize  the  advantage  to  my  con- 
clusions of  the  possible  disadvantage  of  early  finishing. 

The  children  seemed  to  enjoy  the  tests.  I  was  surprised  at 
my  success  in  keeping  their  interest  nearly  the  same  at  all  four 
periods  of  the  school  day,  so  that  their  zeal  in  the  work  would 
be  as  constant  as  possible  and  not  in  favor  of  any  period.  In 
this  way  there  was  eliminated  almost  entirely  the  element  of 
boredom — probably  the  greatest  influence  in  decreasing  the 
quantity  and  quality  of  work  in  the  ordinary  routine  of  the 
school  day.  Studies  of  mental  fatigue  should  be  well  guarded 
against  the  interference  by  boredom,  which  is  often  confused 
with  fatigue,  and  which  has  vitiated  the  results  of  several  ex- 
periments. This  confusion  is  general  in  teachers'  estimates 
of  fatigue  and  renders  them  of  little  value  for  scientific  study. 

The  time  schedule1  was  arranged  so  as  to  test  the  children  at 
approximately  9:10  A.  M.,  11:05  A.  M.,  1:10  P.  M.,  and  2:30 
p.  M. — near  the  opening  (after  a  brief  period  for  settling  down 
to  work)  and  the  close  of  the  morning  and  afternoon  sessions. 
The  exact  time  varied  from  these  points  according  to  the  number 
of  classes  to  be  tested  in  a  day,  the  time  of  my  arrival  in  a 
classroom,  and  the  length  of  preparation  necessary.  The  classes 
in  the  different  schools  were  combined  into  groups  of  four, 
either  one,  two,  or  three  groups  being  tested  in  a  day.  With 
only  one  group  in  P.  S.  1772  the  above  schedule  could  be  closely 
adhered  to ;  but  with  two  groups  a  day  in  P.  S.  27  and  83,  and 
three  groups  in  P.  S.  3,  two  classes  and  three  classes,  re- 
spectively— one  from  each  group — were  tested  in  immediate 
succession  at  each  of  the  four  periods  of  the  school  day. 
The  classes  of  the  second  group  followed  the  corresponding 
classes  of  the  first  group  just  as  soon  as  I  could  get  from  the 

xln  most  classes  there  were  two-minute  formal  gymnastic  drills  at  eleven 
and  two  o'clock.  I  was  unable  to  detect  any  effect  of  these  drills  toward 
increasing  or  decreasing  fatigue;  but  the  eleven  o'clock  drill  may  have 
benefited  the  work  at  the  second  period  to  a  slight  degree. 

2In  this  school  an  extra  class  was  tested  at  an  odd  period  but  had  no 
place  in  my  experiment.  x 


METHOD 


13 


one  classroom  to  the  other  and  start  the  test  with  the  later  class. 
In  P.  S.  3  the  classes  of  the  third  group  followed  those  of  the 
second  group  in  a  similar  time  relationship.  With  two  or 
three  groups  to  he  tested ,  the  fourth  period  was  begun  before 
2.30  P.  M.  so  that  the  work  could  be  completed  before  the 
3  :00  p.  M.  dismissal.  The  following  time  schedule  is  typical : 

Time  Schedule — Public  School  83 — 5B  Classes. 


Group 

Class 

First  Test 

Second  Test 

Third  Test 

Fourth  Test 

Jan.  8 

Jan.  15 

Jan.  22 

Jan.  29 

1 

5B1 

9:12 

11:06 

1:04 

2:24 

2 

5B2 

9:34y2 

ll:22i/3 

1:20 

2:39 

1 

5B3 

11:04 

l:04i/2 

2:23 

9:lli/2 

2 

5B4 

Il:23y2 

1:20 

2:38i/2 

9:26i/2 

1 

5B5 

l:08i/2 

2:25 

9:05i/2 

ll:04i/2 

2 

5B6 

1:29 

2:41 

9:22 

11:22 

1 

5B7 

2:23i/2 

9:08i/2 

11:05 

I:08y2 

2 

5B8 

2:44i/2 

9:26 

11:21 

1:25 

It  is  evident  that  the  time  relationship  of  the  classes 
of  the  first  group  to  each  other  was  almost  the  same  as 
that  of  the  classes  of  the  second,  or  of  the  third,  group  to 
each  other.  The  results  for  my  purpose  were  not  affected  by 
thus  testing  the  classes  of  one  group  after  the  corresponding 
classes  of  a  preceding  group,  because  each  group  constituted  a 
unit  by  itself  for  my  comparison  of  the  four  periods  of  the 
school  day.  In  fact,  the  advantage  of  a  wider  representation 
of  the  morning  and  afternoon  sessions  was  thereby  gained.  For 
instance,  the  tests  with  the  first  groups  about  9  :10  A.  M.,  which 
might  possibly  have  come  in  a  few  classes  before  the  children 
had  settled  down,  were  balanced  in  the  total  results  by  the  tests 
with  the  second  groups  about  9  :2T  A.  M.  However,  a  compari- 
son of  the  fatigue  shown  by  these  groups  gives  no  preference 
to  either  time  for  the  first  period. 

The  most  important  features  of  the  time  schedule  were  the 
balancing  and  consequent  neutralization  of  the  practice  effect 
in  the  second,  third,  and  fourth  tests.  Thereby  the  fatigue 
effect  was  left  free  for  my  comparison  of  the  quantity  and 
quality  of  the  work  at  the  four  periods.  This  was  done  by 
having  each  of  the  four  tests  taken  at  each  of  the  four  periods 
by  one  of  the  four  classes  in  a  group.  The  first  test  was  taken 
at  the  first  period  by  the  first  class,  at  the  second  period  by  the 
second  class,  at  the  third  period  by  the  third  class,  and  at  the 


14  STUDIES  OF  MENTAL  FATIGUE 

fourth  period  by  the  fourth  class;  the  second  test  was  taken 
at  the  first  period  by  the  fourth  class,  at  the  second  period  by 
the  first  class,  at  the  third  period  by  the  second  class,  and  at  the 
fourth  period  by  the  third  class;  the  third  test  was  taken  at 
the  first  period  by  the  third  class,  at  the  second  period  by  the 
fourth  class,  at  the  third  period  by  the  first  class,  and  at  the 
fourth  period  by  the  second  class ;  the  fourth  test  was  taken  at 
the  first  period  by  the  second  class,  at  the  second  period  by 
the  third  class,  at  the  third  period  by  the  fourth  class,  and  at 
the  fourth  period  by  the  first  class.  With  two  groups  to  be 
tested  in  one  day,  the  four  classes  in  the  second  group  followed 
the  above  schedule  about  seventeen  minutes  after  the  correspond- 
ing classes  of  the  first  group.  In  P.  S.  3  the  third  group  fol- 
lowed the  second  group  in  similar  order.  By  such  a  schedule  the 
work  of  the  group  at  each  period  included  all  four  tests  (each 
test  was  generally  taken  a  week  apart),  and  consequently  the 
practice  effect  of  one  class  at  the  second  period,  of  another  class 
at  the  third  period,  and  of  another  class  at  the  fourth  period. 

This  arrangement  was  based  on  the  belief  that,  if  each  test 
were  taken  by  each  class  at  the  same  period,  the  practice  effect 
of  any  one  class  in  the  second,  third,  or  fourth  test  would  be 
almost  equal  to  the  practice  effect  of  any  other  class  in  its 
group  in  the  corresponding  test;  and  that,  as  each  period  in- 
cluded the  practice  effects  in  the  second,  third,  and  fourth  tests, 
the  sum  of  the  three  practice  effects  of  a  group  at  any  one 
period  would  be  balanced  and  neutralized  by  the  sum  of  the 
three  almost  equal  practice  effects  of  the  same  group  at  any 
other  period.  This  belief  in  the  approximate  equality  of  the 
practice  effect  of  the  four  classes  in  a  group  can  not  be  proved 
or  disproved  by  my  results,  because  the  same  test  was  taken 
at  different  periods  by  the  four  classes,  and  the  practice  effect 
of  any  class  was  thereby  complicated  with  a  different  fatigue 
effect  and  rendered  incomparable  with  the  practice  effect  of 
any  other  class  in  its  group  in  the  same  test.  If  there  were 
differences  in  the  practice  effect  of  the  four  classes  in  a  group, 
especially  of  those  classes  at  different  stages  of  advancement, 
they  were  probably  very  slight.  Even  these  differences  were 
partially  neutralized  in  my  total  results,  since  the  classes  in 
different  groups  were  not  tested  in  the  same  order  of  advance- 
ment: in  P.  S.  177  in  ascending  order,  in  P.  S.  -83  on  the 
same  level  of  advancement,  in  P.  S.  27  in  descending  order, 
and  in  P.  S.  3  in  ascending  order.  (As  the  four  half-grades  in 
P.  S.  3  were  divided  into  a,  b,  arid  c  sections  according  to 


GRADING  15 

ability,  these  sections  were  combined  into  a,  b,  and  c  groups; 
and  the  results  show  some  positive  though  not  consistent  corre- 
lation between  ability  and  resistance  to  fatigue.)  This  varia- 
tion gave  a  different  relationship  between  practice  and  fatigue 
effects  in  the  different  groups  according  to  the  periods  at  which 
the  corresponding  tests  were  taken  by  the  more  advanced  and 
by  the  less  advanced  classes. 

The  figures  on  page  26  show  that  the  practice  effect  in  the 
forty  classes  tested  was  small,  especially  because  (1)  an  initial 
interest  partly  balanced  whatever  initial  disadvantage  the 
children  may  have  had  in  the  first  test,  (2)  the  work  was  rapid 
and  short,  (3)  a  week  generally  intervened  between  the  tests, 
and  (4)  no  class  drill  on  the  subject-matter  of  the  tests  was 
allowed.  However,  the  elimination  of  the  practice  effect  from 
my  results  frees  this  experiment  from  the  error  common  to 
most  of  the  experiments  on  mental  fatigue  in  relation  to  the 
daily  school  program. 

The  practice  effect  within  a  single  test  was  not  considered. 
With  tests  having  simple  examples  of  the  same  kind,  such  a 
result  were  possible;  but  with  the  variety  of  examples  in  my 
tests,  both  in  kind  and  in  difficulty,  the  accumulation  of  a 
practice  effect  during  the  ten  minutes  could  hardly  have  taken 
place.  Even  if  there  were  such  practice  effect  in  my  results,  it 
would  have  been  balanced  against  itself  in  my  comparison  of 
the  four  tests  at  the  four  periods. 

GRADING. 

The  papers  were  filed  and  graded,  and  the  results  tabulated, 
according  to  school,  test,  class,  and  name.  Only  full  sets  of 
four  tests  per  child  were  used,  all  partial  sets  being  thrown  out. 
Unless  called  back  to  their  former  class  for  my  work,  the 
children  who  were  removed  to  another  class,  after  one  or  more 
tests,  took  the  remaining  tests  at  wrong  periods,  thus  causing 
all  their  papers  to  be  thrown  out.  In  spite  of  many  absences 
and  removals,  1,153  children  in  the  forty  classes  worked  the 
four  tests  in  proper  order. 

The  grading  of  the  4,612  papers  necessitated  such  tedious 
and  conscientious  attention  to  details,  that  it  was  not  "farmed 
out"  to  others,  who  might  have  been  careless,  but  was  done 
entirely  by  my  wife  and  me.  The  care  taken  to  be  exact  and 
to  go  over  the  papers  again  in  search  for  possible  errors  in 
grading  extended  the  time  for  this  work  to  four  months.  In 


16  STUDIES  OF  MENTAL  FATIGUE 

the  detailed  method  used,  every  figure  the  child  put  down  in 
working  the  examples  was  graded  right  or  wrong,  a  complete 
paper  in  each  test  including  190  figures.  ~No  child  was  given 
a  total  credit  of  right  or  wrong  figures  for  an  example  or  part 
of  an  example  greater  than  that  necessary  for  the  correct  work- 
ing of  that  example  or  that  part,  though  the  mistake  of  a  child 
would  often  involve  a  greater  number  of  figures.  On  the  other 
hand,  the  completion  of  work  on  an  example  or  part  of  an 
example  gave  the  child  the  total  credit  of  right  or  wrong 
figures  for  that  example  or  that  part,  whether  the  child  had 
put  down  that  number  of  figures  or  not.  Misplaced  figures 
were  counted  wrong,  as  were  also  the  omitted  figures  in  those 
examples  that  had  been  worked  by  the  child.  In  addition  to 
these  main  rules  for  grading  the  papers,  there  were  many  sub- 
sidiary and  consistent  rules  for  special  cases,  which  helped 
greatly  in  threading  the  jungle  of  right  and  wrong  figures 
which  a  child  would  sometimes  create. 

Every  method  of  grading  arithmetic  papers  is  open  to  objec- 
tions, but,  for  my  exact  comparison  of  the  work  at  four  periods 
of  the  school  day,  the  detailed  method  used  seemed  far  prefer- 
able. Most  of  the  objections  which  might  be  urged  against 
this  method  would  not  apply  to  the  present  case,  as  the  aim 
was  not  to  give  an  absolute  grading  of  ability  in  the  four 
fundamental  operations,  but  simply  to  be  consistent  in  judging 
the  quantity  and  quality  of  the  work  at  the  four  periods.  It 
might  be  urged  that  the  value  of  the  figures  in  some  examples 
or  parts  of  examples  was  not  equal  to  that  of  those  in  other 
examples  or  parts  of  examples.  But  where  a  child  worked  the 
similar  examples  in  all  four  tests  the  method  of  marking  was 
the  same  for  all  tests,  and  therefore  for  all  periods.  It  is  only 
where  a  child  worked  one  or  more  examples  in  one  or  more 
tests,  but  not  the  similar  examples  in  the  other  tests,  and  where 
the  figures  in  these  particular  examples  could  be  shown  to  be 
r : :  rvalued  in  comparison  with  the  figures  in  those  examples 
t1  •••'{  had  been  worked  in  all  four  tests,  that  the  above-mentioned 
objection  has  any  validity.  The  valuation  of  the  figures  in  the 
ninth  example  in  comparison  with  that  of  those  in  the  fifth, 
in  the  few  cases  where  the  ninth  example  was  worked  by  a 
child  in  some  tests  but  not  in  others,  is  the  only  illustration 
that  might  possibly  affect  my  results  to  more  than  a  negligible 
degree.  Whatever  small  effect  a  possible  disparity  in  the  value 
of  figures  in  these  and  other  examples  might  have  had  upon 
my  results  would  strengthen  my  conclusions  as  to  the  little 


RESULTS  17 

fatigue  shown  in  my  tests,  because  the  subtraction  of  this  effect 
from  the  fatigue  effect  would  lessen,  of  course,  the  signs  of 
fatigue  just  to  that  degree.  In  fact,  I  might  emphasize  the 
advantage  to  my  conclusions  of  this  possible  disparity. 

Another  objection  may  be  made  that  an  initial  wrong  figure 
may  involve  a  series  of  figures  which,  though  wrong,  are  really 
the  correct  consequence  of  the  first  mistake  and  that,  therefore, 
only  the  initial  figure  should  be  counted  wrong.  To  trace  out 
from  every  initial  wrong  figure  in  every  example  in  4,612 
papers  all  the  consequent  figures,  and  to  determine  whether 
the  latter  figures  were  correct  consequences  of  the  former,  would 
be  an  interminable  task.  Even  then  there  would  never  be  cer- 
tainty that  the  consequent  figures,  in  individual  papers,  did  not 
include  more  initial  wrong  figures  than  the  first  one.  As  the 
necessary  thing  in  my  experiment  was  to  grade  consistently  the 
work  at  all  four  periods,  and,  as  every  figure  was  graded  accord- 
ing to  the  same  rules  for  these  periods,  the  change  suggested, 
even  if  possible,  would  not  have  affected  my  results. 

In  order  to  strengthen  my  comparison  of  the  work  at  the 
four  periods  by  using  two  different  methods  of  grading,  rather 
than  one  alone,  all  the  papers  were  graded  again  by  a  gross 
method  in  which  only  the  answers  were  considered.  The  gross 
method  chosen  was  very  similar  to  that  used  by  Mr.  Courtis. 
The  first  and  second  examples  were  together  credited  with  one 
point,  this  point  being  counted  wrong  on  account  of  one  or 
more  mistakes  in  either  example ;  the  third,  fourth,  fifth,  sixth, 
and  tenth  examples  were  each  credited  with  one  point,  the 
point  for  a  given  example  being  counted  wrong  on  account  of 
one  or  more  mistakes  in  that  example;  the  seventh,  eighth, 
ninth,  eleventh,  and  twelfth  examples  were  each  credited  with 
two  points,  one  point  for  a  given  example  being  counted  wrong 
on  account  of  one  mistake,  and  two  points  being  counted  wrong 
on  account  of  two  or  more  mistakes  in  that  example. 

RESULTS. 

After  the  results  for  each  child  were  graded  by  the  detailed 
method  and  tabulated,  the  number  of  right  and  wrong  figures 
for  each  class  in  each  test  was  averaged,  and  then  the  number 
of  right  and  wrong  figures  for  each  group  of  four  classes  at 
each  of  the  four  periods  of  the  school  day.  The  individual 
variations  in  the  children  were  first  merged  in  the  class  aver- 


18 


STUDIES  OF  MENTAL  FATIGUE 


ages  and  again  in  the  group  averages.     From 
were  made  tables  for  each  of  the  ten  groups, 
table  is  typical: 


these 

The  following 


Table  of  Results — Group  2 — Public  School  27. 


00 

5 

£ 

FIRST    PERIOD 

SECOND    PERIOD 

THIRD    PERIOD 

FOURTH    PERIOD 

Test 

Eight 

Wrong 

Test 

Right 

Wrong 

Test 

Right 

Wrong 

Test 

Right 

Wrong 

5B1 
5A1 
4B2 

4A2 
4 

26 
43 
32 
26 
127 

1 

4 
3 
2 

129.69 
149.07 
131.53 
112.08 
130.59 

14.92 
15.98 
17.53 
20.65 
17.27 

2 
1 

4 
3 

132.35 
126.98 
122.72 
126.69 
127.18 

25.31 
12.12 

24.84 
24.69 
21.74 

3 
2 
1 
4 

142.77 
142.16 
109.56 
122.96 
129.36 

23.42 
21.44 
22.25 

28.35 
23.86 

4 
3 
2 

1 

140.31 
145.28 
124.50 
101.88 
127.99 

25.27 
20.21 
20.47 
23.58 
22.38 

Sum     o 
wrong 
Relative 
Per  cen 
Eelati 
right 

f    right    and 

147 

.86 
.00 
.32 

00 

148.92 
100.72 
85.40 

96.69 

153.22 
103.63 
84.43 

95.64 

150.37 
101.70 
85.12 

96.38 

amouD 
:  right 
ve  pe 

t  done  100 
88 

r  cent 
.   100 

These  tables  gave  answers  to  two  questions,  which  formed 
the  core  of  the  investigation.  The  answer  to  first  question, 
What  was  the  difference  in  the  quantity  of  work  done  at  the 
four  periods?,  was  reached  by  getting  the  sum  of  right  and 
wrong  figures  at  each  period,  by  giving  the  value  of  100.00  to 
the  sum  at  the  first  period  (of  course  any  other  period  could 
have  been  taken  as  the  standard  of  comparison),  and  then  by 
calculating  the  per  cents  of  this  sum  represented  by  the  sum  at 
each  of  the  other  three  periods.  These  per  cents  for  the  ten 
groups  were  as  follows,  the  per  cent  for  the  first  period  being 
100.00  in  every  group: 


Group 

School 

Second  Period 

Third  Period 

Fourth  Period 

1 

177 

103.16 

101.36 

103.19 

2 

27 

100.72 

103.63 

101.70 

3 

27 

100.14 

98.28 

96.62 

4 

83 

100.49 

100.37 

105.81 

5 

83 

98.85 

98.60 

104.05 

6 

83 

102.42 

101.65 

103.52 

7 

83 

102.15 

102.17 

101.87 

8 

3 

101.41 

101.20 

103.74 

9 

3 

101.05 

104.40 

99.99 

10 

3 

104.34 

104.26 

104.54 

RESULTS 


19 


The  answer  to  the  second  question,  What  was  the  difference 
in  the  quality  of  work  done  at  the  four  periods?,  was  reached 
by  calculating  the  per  cent  right  of  the  sum  of  right  and  wrong 
figures  at  each  period,  by  giving  the  value  of  100.00  to  the 
per  cent  right  at  the  first  period,  and  then  by  calculating  the 
per  cent  of  this  per  cent  right  represented  by  the  per  cent  at 
each  of  the  other  three  periods.  These  per  cents  for  the  ten 
groups  were  as  follows,  the  per  cent  for  the  first  period  being 
100.00  in  every  case : 


Group 

School 

Second  Period 

Third  Period 

Fourth  Period 

1 

177 

97.53 

97.58 

97.37 

2 

27 

96.69 

95.64 

96.38 

3 

27 

98.86 

97.34 

97.54 

4 

83 

100.39 

98.65 

97.94 

5 

83 

98.92 

96.90 

95.89 

6 

83 

97.64 

100.94 

98.65 

7 

83 

97.81 

99.12 

98.91 

8 

3 

101.74 

101.39 

100.52 

9 

3 

98.75 

99.15 

97.45 

10 

3 

96.75 

99.06 

97.08 

In  quantity  of  work  done  (sum  of  right  and  wrong  figures) 
as  compared  with  the  first  period,  seven  of  the  ten  groups  tested 
showed  an  increase  at  three  periods,  one  an  increase  at  two 
periods  and  a  decrease  at  one  period,  and  two  an  increase  at 
one  period  and  a  decrease  at  two  periods.  In  all,  there  were 
twenty-five  cases  of  increase,  averaging  2.53  per  cent;  and 
five  cases  of  decrease,  averaging  1.53  per  cent.  The  same  facts 
by  periods  were  as  follows:  at  the  second  period  an  average 
increase  of  1.76  per  cent  in  nine  groups  and  a  decrease  of  1.15 
per  cent  in  one;  at  the  third  period  an  average  increase  of  2.38 
per  cent  in  eight  groups  and  an  average  decrease  of  1.56  per 
cent  in  two;  at  the  fourth  period  an  average  increase  of  3.55 
per  cent  in  eight  groups  and  an  average  decrease  of  1.69  per 
cent  in  two. 

In  quality  of  work  done  (per  cent  of  sum  right)  as  compared 
with  the  first  period,  seven  of  the  ten  groups  tested  showed  a 
decrease  at  three  periods,  two  a  decrease  at  two  periods  and 
an  increase  at  one  period,  and  one  an  increase  at  all  periods. 
In  all,  there  were  twenty-five  cases  of  decrease,  averaging  2.26 
per  cent,  and  five  cases  of  increase  averaging  1.00  per  cent. 
(The  five  cases  of  increase  in  quality  occurred  in  different 
groups  from  those  having  the  five  cases  of  decrease  in  quantity ; 
consequently  there  was  no  connection  between  them.)  The 


20  STUDIES  or  MENTAL  FATIGUE 

same  facts  by  periods  were  as  follows:  At  the  second  period 
an  average  decrease  of  2.13  per  cent  in  eight  groups  and  an 
average  increase  of  1.06  per  cent  in  two  groups;  at  the  third 
period  an  average  decrease  of  2.07  per  cent  in  eight  groups  and 
an  average  increase  of  1.16  per  cent  in  two  groups;  at  the 
fourth  period  an  average  decrease  of  2.53  per  cent  in  nine 
groups  and  an  increase  of  0.52  per  cent  in  one  group.1 

The  most  important  summary  of  results  is  shown  in  the  total 
table  combining  the  forty  classes  of  the  ten  groups  tested,  in 
which  individual,  class,  and  group  variations  were  all  merged. 
The  average  of  the  forty  class  averages  for  each  period  was 
used  as  the  material  for  calculating  the  comparative  per  cents 
of  quantity  and  quality  exactly  in  the  same  way  that  the  aver- 
age of  four  class  averages  for  each  period  was  used  in  a  table 
for  each  single  group.2  The  balanced  relation  to  each  other 
of  the  four  classes  in  each  group  was  not  disturbed  by  this  com- 
bination, which  tended,  however,  to  neutralize  whatever  chance 
variations  may  have  occurred  in  the  single  groups.?  In  quantity 
of  work  done  (sum  of  right  and  wrong  figures}  as  compared 
with  the  first  period  of  the  school  day,  the  ten  groups  together 
showed  a  respective  increase  of  1.51,  1.6J+,  and  2.36  per  cent 
at  the  second,  third,  and  fourth  periods;  and  in  quality  of  work 
done  (per  cent  of  sum  right)  a  respective  decrease  of  1.51,  1.^1, 
and  2.22  per  cent  at  the  second,  third,  and  fourth  periods.  For 
comparison  with  these  results,  obtained  by  the  detailed  method 
of  grading,  a  similar  total  table  was  made  with  the  class  aver- 
ages by  the  gross  method  of  grading,  and  the  following  per 
cents  were  calculated:  In  quantity  of  work  done  (sum  of  right 
and  wrong  points)  as  compared  with  the  first  period,  the  ten 
groups  together  showed  a  respective  increase  of  1.92,  1.31,  and 
2.21  at  the  second,  third,  and  fourth  periods;  and  in  quality 
of  work  done  (per  cent  of  sum  right)  a  respective  decrease  of 

^n  order  to  give  also  the  results  by  schools,  the  first  and  second  groups 
of  P.  S.  27,  of  P.  S.  83-5A,  and  of  P.  S.  83-5B,  and  the  first,  second,  and 
third  groups  of  P.  S.  3,  were  combined  into  four  tables  by  getting  the 
group  averages  for  each  period  of  the  eight  or  twelve  class  averages  in  the 
groups  combined,  and  calculating  therewith  the  comparative  per  cent  of 
quantity  and  quality  exactly  in  the  same  way  as  in  the  single  groups. 

2The  average  of  the  forty  class  averages  was  used  instead  of  the  average 
of  the  ten  group  averages,  as  being  more  representative  of  the  total  con- 
ditions; but  the  difference  between  the  two  total  averages  would  be  very 
small. 


RESULTS  21 

5.74*  4-56,  and  6.66  at  the  second,  third,  and  fourth  periods.1 
The  per  cents  of  increase  in  quantity  in  the  two  tables  are  sur- 
prisingly similar;  the  per  cents  of  decrease  in  quality  in  the 
second  table  are  a  little  over  three  times  as  large  as  those  in 
the  first  table,  but  are  still  very  small.  This  difference  is 
probably  due  to  the  greater  weight  given  errors  by  the  gross 
method  of  grading,  one  error  in  the  answer  to  any  example 
making  wrong  one  point  out  of  a  total  of  sixteen  points  for 
the  entire  test.  This  seems  to  me  a  defect  natural  to  any  gross 
method  of  grading  for  purposes  of  scientific  study.  (Notice 
the  difference  in  the  per  cents  of  decrease  in  quality  in  the 
practice  results  on  page  26.)  However,  it  would  be  inevitable 
that  any  two,  or  any  three,  methods  of  grading  would  show 
some  differences  in  results.  The  two  total  tables  are  given 
herewith.  The  one  for  the  gross  method  of  grading  contains, 
of  course,  all  the  class  averages  necessary  to  make  out  the  single 
table  for  each  group ;  but  this  extra  work  was  not  needed  and 
therefore  was  not  undertaken. 


Subtracting  the  four  classes  of  P.  S.  177,  as  suggested  on  page  12,  we 
have  for  thirty-six  classes,  by  the  detailed  method  of  grading,  an  increase 
of  1.35,  1.68,  and  2.24  per  cent,  respectively,  in  quantity,  and  a  decrease 
of  1.39,  1.26,  and  2.17  per  cent,  respectively,  in  quality;  by  the  gross 
method  of  grading  an  increase  of  1.70,  1.52,  and  1.97  per  cent,  respectively, 
in  quantity,  and  a  decrease  of  6.31,  4.41,  and  6.59  per  cent,  respectively, 
in  quality. 


9,9, 


STUDIES  OF  MENTAL  FATIGUE 


Forty  Classes  (Ten  Groups)  Combined  Into  One  Group. 
Detailed  Method  of  Grading. 


D. 

3 

"o 

Q 

GO 

S3 

FIRST  PERIOD 

SECOND  PERIOD 

THIRD  PERIOD 

FOURTH  PERIOD 

1 

1 

02 

0 

1 

Test 

Eight 

Wrong 

Test 

Eight 

Wrong 

Test 

Eight 

Wrong 

Test 

Eight 

Wrong 

1 

177 

5A1 

29 

1 

150.34 

10.59 

2 

155.28 

23.17 

3 

162.07 

16.31 

4 

167.79 

19.14 

2 

27 

5B1 

26 

129.27 

15.35 

2 

131.96 

25.31 

3 

142.77 

23.42 

4 

140.31 

25.27 

3 

27 

5B2 

25 

135.80 

15.52 

2 

142.76 

26.56 

3 

144.36 

27.48 

4 

137.36 

28.56 

4 

83 

5A1 

35 

99.09 

19.00 

2 

108.09 

16.94 

3 

113.26 

19.60 

4 

116.97 

28.86 

5 

83 

5A2 

37 

92.22 

19.51 

2 

103.57 

19.19 

3 

109.16 

21.49 

4 

109.57 

27.24 

6 

83 

5B1 

36 

100.47 

12.69 

2 

110.33 

16.72 

3 

123.42 

11.28 

4 

119.78 

17.19 

7 

83 

5B2 

32 

114.12 

9.91 

2 

117.41 

19.91 

3 

126.06 

14.16 

4 

123.78 

15.06 

8 

3 

5Aa 

28 

1 

110.11 

15.46 

2 

115.86 

17.54 

3 

125.14 

15.68 

4 

127.54 

18.18 

9 

3 

5Ab 

19 

1 

109.89 

23.74 

2 

115.47 

23.32 

3 

130.37 

29.16 

4 

112.79 

30.76 

10 

3 

5Ac 

19 

1 

92.95 

14.05 

2 

96.42 

24.11 

3 

113.79 

21.89 

4 

101.47 

25.16 

1 

177 

5B1 

38 

4 

159.67 

11.34 

155.68 

12.42 

2 

158.53 

11.11 

3 

164.32 

10.53 

2 

27 

5A1 

43 

4 

148.81 

16.58 

126.93 

12.16 

2 

142.88 

21.70 

3 

144.88 

20.21 

3 

27 

5A2 

31 

4 

153.16 

17.71 

138.13 

12.06 

2 

144.00 

21.00 

3 

151.84 

22.06 

4 

83 

5A3 

38 

4 

102.92 

20.89 

92.63 

16.08 

2 

99.05 

18.79 

3 

112.92 

17.71 

5 

83 

5A4 

26 

4 

110.46 

25.81 

87.62 

18.12 

2 

98.35 

25.81 

3 

111.19 

25.92 

6 

83 

5B3 

28 

4 

111.86 

18.43 

100.32 

15.61 

2 

110.68 

15.50 

3 

112.43 

18.89 

7 

83 

5B4 

27 

4 

114.78 

20.15 

98.63 

18.30 

2 

113.07 

18.26 

3 

118.96 

21.00 

8 

3 

5Ba 

29 

4 

132.14 

16.93 

126.17 

15.14 

2 

127.59 

20.66 

3 

133.07 

17.79 

9 

3 

5Bb 

23 

4 

126.43 

24.43 

116.04 

25.96 

2 

122.30 

29.00 

3 

123.74 

23.26 

10 

3 

5Bc 

15 

4 

106.67 

28.00 

106.13 

26.60 

2 

113.40 

28.87 

3 

111.20 

32.60 

1 

177 

5Ea 

40 

3 

164.60 

8.92 

4 

158.17 

13.35 

1 

136.35 

16.15 

2 

143.62 

16.07 

2 

27 

4B2 

32 

3 

131.66 

17.56 

4 

122.53 

24.84 

1 

109.22 

22.56 

2 

123.87 

21.03 

3 

27 

4B3 

27 

3 

137.37 

22.85 

4 

130.33 

31.59 

1 

113.37 

22.89 

2 

123.48 

25.15 

4 

83 

5A5 

40 

3 

107.42 

20.07 

4 

106.60 

24.40 

1 

93.12 

18.00 

2 

105.47 

23.05 

5 

83 

5A6 

29 

3 

116.59 

13.14 

4 

117.41 

17.90 

1 

90.14 

17.62 

2 

105.79 

19.01 

6 

83 

5B5 

25 

3 

110.60 

11.80 

4 

106.04 

20.60 

1 

89.24 

11.04 

2 

107.00 

18.04 

7 

83 

5B6 

27 

3 

108.15 

20.26 

4 

108.63 

22.56 

1 

95.04 

19.59 

2 

104.07 

21.44 

8 

3 

6Aa 

30 

3 

155.97 

14.47 

4 

156.93 

12.83 

1 

151.90 

9.97 

2 

152.77 

18.20 

9 

3 

6Ab 

34 

3 

149.76 

15.68 

4 

143.68 

20.91 

1 

136.03 

19.50 

2 

138.85 

21.91 

10 

3 

6Ac 

24 

3 

126.04 

21.50 

4 

120.29 

31.00 

1 

112.21 

24.29 

2 

122.12 

25.54 

1 

177 

5Eb 

31 

2 

152.26 

13.71 

3 

161.61 

13.00 

4 

163.10 

16.94 

1 

154.16 

17.23 

2 

27 

4A2 

26 

2 

112.08 

20.65 

3 

126.65 

24.73 

4 

122.96 

28.35 

1 

101.88 

23.58 

3 

27 

4A3 

25 

2 

101.88 

31.96 

3 

114.12 

22.12 

4 

105.92 

27.60 

1 

86.56 

20.48 

4 

83 

5A7 

29 

2 

99.31 

14.17 

3 

105.00 

19.45 

4 

99.28 

23.55 

1 

88.21 

17.72 

5 

83 

5A8 

29 

2 

94.79 

11.86 

3 

96.28 

18.72 

4 

97.93 

17.07 

1 

86.52 

18.72 

6 

83 

5B7 

26 

2 

122.50 

16.73 

3 

128.77 

18.92 

4 

133.73 

18.50 

1 

113.46 

16.46 

7 

83 

5B8 

21 

2 

115.95 

16.86 

3 

127.95 

18.00 

4 

124.57 

20.71 

1 

109.62 

15.95 

8 

3 

6Ba 

28 

2 

140.07 

20.07 

3 

156.43 

12.86 

4 

147.64 

13.86 

1 

147.89 

12.39 

9 

3 

6Bb 

25 

2 

128.80 

17.36 

3 

138.64 

18.32 

4 

144.32 

11.68 

1 

126.36 

18.40 

10 

3 

6Bc 

21 

2 

130.19 

21.71 

3 

137.38 

22.67 

4 

131.43 

18.24 

1 

127.86 

19.71 

40 

1,153 

122.68 

17.69 

122.72 

19.85 

122.94 

19.73 

122.79 

20.89 

Sum     of    right    and 

wrong  .   .  .                   140  37 

142.57 

142.67 

143.68 

Relative  amount  done  100.00 

101.57 

101.64 

102.36 

Per  cent  right  87.40 

86.08 

86.17 

85.46 

Relative  per  cent  right  100.00 

98.49 

98.59 

97.78 

RESULTS 


23 


Forty  Classes  (Ten  Groups)  Combined  Into  One  Group. 
Gross  Method  of  Grading. 


e. 

73 

£ 

FIRST  PERIOD 

SECOND  PERIOD 

THIRD  PERIOD 

FOURTH  PERIOD 

D 

o 

i 

1 

O 

1 

3 

i 

Test 

Bight 

Wrong 

Test 

Right 

Wrong 

Test 

Eight 

Wrong 

Test 

Right 

Wrong 

1 

177 

5A1 

29 

1 

11.38 

2.21 

2 

10.69 

3.90 

3 

11.28 

3.62 

4 

11.66 

3.79 

2 

27 

5B1 

26 

1 

9.23 

2.96 

2 

8.58 

4.35 

3 

9.27 

4.54 

4 

9.00 

4.65 

3 

27 

5B2 

25 

1 

9.40 

3.28 

2 

9.20 

5.00 

3 

8.92 

5.36 

4 

8.48 

5.20 

4 

83 

5A1 

35 

1 

6.14 

2.89 

2 

6.51 

3.80 

3 

6.91 

3.71 

4 

7.11 

4.66 

5 

83 

5A2 

37 

1 

6.03 

3.24 

2 

6.38 

3.43 

3 

6.46 

4.62 

4 

6.49 

4.84 

6 

83 

5B1 

36 

1 

6.56 

2.22 

2 

7.33 

2.75 

3 

8.44 

2.47 

4 

7.92 

3.33 

7 

83 

5B2 

32 

1 

7.28 

2.62 

2 

7.28 

4.16 

3 

8.62 

3.16 

4 

7.84 

3.87 

8 

3 

5Aa 

28 

1 

7.57 

2.50 

2 

7.21 

3.75 

3 

8.46 

3.25 

4 

7.89 

3.64 

9 

3 

5Ab 

19 

1 

7.11 

4.32 

2 

7.42 

4.37 

3 

7.89 

5.32 

4 

5.84 

5.79 

10 

3 

5Ac 

19 

1 

5.79 

2.26 

2 

5.47 

4.63 

3 

6.89 

4.53 

4 

6.16 

4.32 

1 

177 

5B1 

38 

4 

11.42 

2.76 

1 

10.92 

3.18 

2 

11.76 

1.87 

3 

11.66 

2.84 

2 

27 

5A1 

43 

4 

10.30 

3.33 

1 

8.35 

3.12 

2 

9.47 

4.07 

3 

8.84 

4.79 

3 

27 

5A2 

31 

4 

10.10 

3.90 

1 

9.61 

3.00 

2 

9.74 

3.90 

3 

9.52 

4.90 

4 

83 

5A3 

38 

4 

6.76 

2.87 

1 

5.82 

2.39 

2 

6.13 

3.32 

3 

7.18 

3.68 

5 

835A4 

26 

4 

6.92 

3.88 

1 

5.15 

3.08 

2 

5.77 

3.92 

3 

6.42 

4.96 

6 

83 

5B3 

28 

4 

7.46 

3.04 

1 

6.14 

3.07 

2 

7.11 

3.04 

3 

7.07 

3.54 

7 

83 

5B4 

27 

4 

7.04 

3.96 

1 

5.85 

3.78 

2 

7.26 

3.33 

3 

6.93 

4.15 

8 

3 

5Ba 

29 

4 

8.59 

3.48 

1 

7.48 

3.72 

2 

8.28 

3.83 

3 

8.07 

4.07 

9 

3 

5Bb 

23 

4 

7.61 

4.65 

1 

6.57 

4.78 

2 

7.30 

4.83 

3 

7.57 

4.48 

10 

3 

5Bc 

15 

4 

6.80 

4.33 

1 

6.73 

4.27 

2 

6.13 

5.53 

3 

6.53 

5.27 

1 

111 

5Ea 

40 

3 

11.92 

2.42 

4 

11.52 

2.92 

1 

9.20 

3.20 

2 

10.37 

3.02 

2 

27 

4B2 

32 

3 

8.59 

3.72 

4 

7.16 

4.91 

1 

6.12 

4.34 

2 

7.84 

4.06 

3 

27 

4B3 

27 

3 

8.74 

4.30 

4 

8.07 

5.37 

1 

6.67 

4.44 

2 

7.70 

4.37 

4 

83 

5A5 

40 

3 

5.90 

4.20 

4 

6.67 

3.80 

1 

5.67 

2.50 

2 

6.65 

3.07 

5 

83 

5A6 

29 

3 

7.79 

2.62 

4 

7.59 

3.31 

1 

5.59 

2.45 

2 

7.00 

3.00 

6 

83 

5B5 

25 

3 

7.20 

2.80 

4 

6.80 

3.64 

1 

5.16 

2.40 

2 

6.12 

3.60 

7 

83 

5B6 

27 

3 

7.48 

2.85 

4 

7.07 

3.44 

1 

5.96 

3.19 

2 

6.67 

3.19 

8 

3 

6Aa 

30 

3 

10.77 

3.43 

4 

10.57 

3.47 

1 

10.97 

2.40 

2 

10.63 

3.60 

9 

3 

6Ab 

34 

3 

9.71 

4.21 

4 

9.41 

4.00 

1 

8.76 

4.24 

2 

9.29 

4.00 

10 

3 

6Ac 

24 

3 

8.21 

4.17 

4 

6.96 

5.29 

1 

7.25 

3.92 

2 

7.00 

5.00 

1 

177 

5Eb 

31 

2 

11.45 

2.39 

3 

11.13 

3.23 

4 

11.32 

3.35 

1 

10.74 

3.71 

2 

27 

4A2 

26 

2 

7.23 

3.27 

3 

7.62 

4.69 

4 

7.50 

4.58 

1 

6.31 

3.42 

3 

27 

4A3 

25 

2 

6.12 

4.72 

3 

7.20 

3.96 

4 

6.04 

4.48 

1 

5.32 

3.08 

4 

83 

5A7 

29 

2 

6.14 

2.93 

3 

6.86 

3.72 

4 

6.17 

4.03 

1 

5.34 

2.79 

5 

83 

5A8 

29 

2 

6.17 

2.52 

3 

5.66 

3.41 

4 

5.66 

3.24 

1 

5.34 

3.03 

6 

83 

5B7 

26 

2 

8.65 

2.65 

3 

8.12 

4.04 

4 

9.35 

3.27 

1 

7.35 

3.15 

7 

83 

5B8 

21 

2 

8.33 

2.52 

3 

8.90 

3.05 

4 

8.24 

3.38 

1 

7.05 

3.14 

8 

3 

6Ba 

28 

2 

9.39 

3.79 

3 

10.46 

3.50 

4 

9.64 

3.36 

1 

10.25 

2.96 

9 

3 

6Bb 

25 

2 

8.24 

3.72 

3 

8.48 

4.52 

4 

9.72 

3.32 

1 

8.04 

3.76 

10 

3 

6Bc 

21 

2 

8.95 

3.76 

3 

8.62 

4.48 

4 

8.48 

3.90 

1 

8.43 

3.95 

40 

1,153 

8.16 

3.29 

7.84 

3.83 

7.89 

3.71 

7.79 

3.92 

Sum     of    right     and 

wrong    11  .  45 

11  67 

11.60 

11.71 

Relative  amount  done  100.00 

101.92 

101.31 

102.27 

Per  cent  right  71  27 

67.18 

68.02 

66.52 

Relative  per  cent  right  100.00 

94.26 

95.44 

93.34 

24  STUDIES  OF  MENTAL  FATIGUE 

The  following  diagram  illustrates  these  comparative  per 
cents  of  increase  in  quantity  (above  the  heavy  horizontal  line) 
and  of  decrease  in  quality  (below  the  heavy  horizontal  line). 
The  continuous  lines  represent  the  results  by  the  detailed 
method  of  grading,  and  the  dotted  lines  the  results  by  the  gross 
method  of  grading. 


l  i 


B 


/oo.oo 


Increase 

in 
Quantity 

/oo.oo 


Decrease 

in 
Quality 


In  these  two  series  of  per  cents  are  apparently  opposing 
results — a  fairly  continuous  increase  in  quantity  of  work  done 
at  the  four  successive  periods,  with  a  very  small  increase  in  the 
second  table  at  the  third  period;  and  a  fairly  continuous 
decrease  in  quality,  with  a  very  small  increase  in  the  first 
table  and  a  small  increase  in  the  second  table  at  the  third 
period.  (These  variations  at  the  third  period  were  due  to  the 
influence  of  the  intermission  from  twelve  to  one  o'clock. )  How- 
ever, this  opposition  may  be  more  apparent  than  real.  Fatigue 
often  shows  itself  in  a  weakening  of  that  inhibition  which  as- 
sures slower  but  more  careful  and  consequently  more  correct 
work,  the  speed  of  the  fatigued  worker  generally  being  a  sign 
of  decreased  efficiency.  (This  result  is  evident  in  many 


RESULTS  25 

different  experiments.)  But  a  claim  that  all  the  above- 
mentioned  increase  in  quantity  is  due  to  fatigue  would  be  a 
biased  interpretation,  though  the  influence  of  the  noon  inter- 
mission in  arresting  the  increase  at  the  third  period  and  the 
presence  of  the  greatest  increase  at  the  fourth  period  strengthen 
this  claim.  It  is  possible  that  some  of  the  increase  may  be  due 
to  increased  efficiency  as  the  day  advances,  the  children  becom- 
ing more  habituated  to  school  work — having  a  greater  "swing," 
as  Offner  says.  The  decrease  in  quality  of  work  done  at  the 
four  successive  periods  may  more  justly  be  considered  as  due 
almost  entirely  to  fatigue,  which  is  arrested  by  the  noon  inter- 
mission but  is  greatest  at  the  fourth  period.  A  slight  boredom 
and  consequent  carelessness  as  the  day  advances  may  have 
affected  the  results  in  spite  of  my  efforts  to  keep  the  interest 
nearly  the  same  at  all  four  periods.  Altogether,  we  may  con- 
sider that  most,  though  not  all,  of  this  increase  in  quantity 
and  decrease  in  quality  is  a  sign  of  fatigue. 

It  is  impossible  to  combine  accurately  into  one  series  for 
each  table  the  per  cents  of  quantity  and  of  quality  at  each  of 
the  four  periods  in  order  to  make  a  single  comparison  of  the 
work  done.  Any  such  combination,  though  arbitrary,  ought 
to  be  based  upon  a  just  proportion  of  value  between  the  two 
series.  For  instance,  one  per  cent  of  increase  in  quantity 
should  not  cancel  one  per  cent  of  decrease  in  quality  because 
the  latter  per  cent  has  more  value  than  the  former,  more 
weight  in  grading  ability.  A  suggestive  proportion  is  that 
based  upon  the  per  cents  right  of  the  sum  of  right  and  wrong 
figures  (or  points)  at  the  second,  third,  and  fourth  periods, 
these  being  in  the  first  table  86.06,  86.17,  and  85.46  per 
cent,  respectively.  These  per  cents  give  a  ratio  of  value  of 
1.00:. 8608  between  the  sum  and  the  per  cent  right  at  the 
second  period,  a  ratio  of  1.00:  .8617  at  the  third  period,  and 
a  ratio  of  1.00:. 8546  at  the  fourth  period.  For  the  second 
period  we  multiply  the  1.57  per  cent  in  quantity  by  .8608 
and  the  1.51  per  cent  in  quality  by  1.00,  in  order  to  reduce 
the  per  cents  to  equal  value,  and  get  1.35  and  1.51  per  cent, 
respectively.  By  subtracting  the  per  cent  of  increase  in 
quantity  from  the  per  cent  of  decrease  in  quality,  we  get  a 
remaining  decrease  of  .16  per  cent.  This  gives  99.84  as  the 
combined  per  cent  of  quantity  and  quality  at  the  second  period. 
In  the  same  way  we  get  100.00  as  the  combined  per  cent  at  the 
third  period  and  99.80  at  the  fourth.  The  combined  per  cents 
in  the  second  table  are  95.55,  96.33,  and  94.85  for  the  second, 


26  STUDIES  OF  MENTAL 

third,  and  fourth  periods,  respectively.  It  might  be  objected 
that,  as  both  the  increase  in  quantity  and  the  decrease  in  quality 
are  mainly  due  to  fatigue,  they  should  not  be  balanced  against 
each  other  and  only  the  remainder  be  subtracted  from  the 
100.00  per  cent  standard  of  the  first  period.  One  might  even 
go  so  far  as  to  suggest  subtracting  from  this  100.00  per  cent 
standard  the  sum  of  the  per  cents  of  increase  and  decrease. 
The  reply  is  that  the  per  cents  of  comparison  must  be  based 
upon  the  actual  work  done,  not  upon  an  interpretation  of  the 
causes  thereof,  and  that  in  grading  such  work  an  increase  in 
quantity  would  naturally  tend  to  offset  a  decrease  in  quality 
and  vice  versa,  whether  or  not  both  the  increase  and  the  de- 
crease could  be  attributed  to  one  cause.  However,  my  sug- 
gested combination  may  show  too  little  fatigue  and  is  offered 
simply  as  an  illustration  of  a  possible  method  of  reaching  one 
series  of  per  cents  for  purposes  of  comparison. 

The  practice  effect  was  calculated  by  rearranging  the  figures 
in  the 'two  total  tables  in  columns  according  to  tests  rather  than 
periods.  As  each  test  was  given  forty  times — ten  times  at  each 
of  the  four  periods — the  total  result  for  each  test  combined  the 
work  at  each  of  the  four  periods  and  thus  neutralized  the  fatigue 
effect,  which  has  often  influenced  the  results  in  practice  experi- 
ments. These  total  results  were  compared  to  find  the  practice 
effect.  By  the  detailed  method  of  grading,  in  quantity  of  work 
(sum  of  right  and  wrong  figures)  as  compared  with  the  first  test, 
the  ten  groups  together  showed  a  respective  increase  of  8.91, 
14.09,  and  13.67  per  cent  in  the  second,  third,  and  fourth  tests; 
in  quality  of  work  done  (per  cent  of  sum  right)  a  respective  de- 
crease of  1.35  and  1.31  per  cent  in  the  second  and  fourth  tests, 
and  an  increase  of  0.46  per  cent  in  the  third  test.  By  the  gross 
method  of  grading,  in  quantity  of  work  done  (sum  of  right 
and  wrong  points)  as  compared  with  the  first  test,  the  ten 
groups  together  showed  a  respective  increase  of  8.97,  15.39, 
and  13.97  per  cent  in  the  second,  third,  and  fourth  tests;  and 
in  quality  of  work  done  (per  cent  of  sum  right)  a  respective 
decrease  of  2.00,  2.28,  and  3.20  per  cent  in  the  second,  third, 
and  fourth  tests. 


SECOND  STUDY 

The  tests  were  given  in  February  and  March,  1913,  to  sixteen 
classes,  573  pupils,  in  three  Lynchburg,  Va.,  schools.  The  im- 
portant difference  between  this  experiment  and  that  in  New 
York  City  is  the  amount  of  continuous  work  required  by  the 
tests.  The  New  York  classes  were  given  four  ten-minute  tests 
at  four  periods  of  the  school  day,  the  Lynchburg  classes  two 
twenty-five  minute  tests  at  two  periods.1  The  subject  matter 
used  was  the  same  in  both  experiments,  but  the  Lynchburg 
classes  took  two  tests  as  one.  The  reason  for  this  extension  of 
time  was  the  supposition  that  a  ten-minute  spurt  might  not  reveal 
the  amount  of  fatigue  present,  the  pupils  working  the  short  test 
with  fairly  unform  efficiency  at  four  periods  of  the  school  day. 
A  continuous  application  for  twenty-five  minutes  could  hardly 
fail  to  reveal  most  of  the  fatigue  present  at  the  time  of  starting 
the  test  and  the  further  possible  fatigue  from  the  longer  test 
itself.  If  the  fatigue  from  the  test  itself  were  equally  present  in 
the  morning  and  in  the  afternoon  work,  it  would  be  neutralized 
in  the  results;  but  if  it  were  greater  in  the  afternoon  on  ac- 
count of  greater  fatigue  at  the  time  of  starting,  the  difference 
would  be  evident  in  the  results.  The  longer  test,  therefore,  has 
two  possibilities  of  revealing  fatigue  and  is  also  a  better  illus- 
tration of  the  time  required,  though  with  less  continuous  pres- 
sure, for  study  and  recitation  in  actual  school  practice. 

The  Lynchburg  tests  were  given  on  February  25  and  27, 
1913,  to  the  5A,  5B,  6A,  and  6B  classes  in  Biggers  School;  on 
February  26  and  28  to  the  5A,  5B,  6A,  and  6B  classes  in  Mon- 
roe School;  on  March  11  and  13  to  the  7B,  7A,  6B,  and  6A1 
classes  in  Federal  School;  on  March  12  and  14  to  the  6A2, 
5Bl,  5B2,  and  5 A  classes  in  Federal  School.  The  weather  was 
mild,  and  window  ventilation  was  used  in  addition  to  the  fur- 
nace system.  The  schools  had  a  one-session  day,  with  a  fifteen- 
minute  recess  soon  after  the  morning  tests  and  a  twenty  (some- 
times fifteen)  minute  recess  before  the  afternoon  tests.  During 
the  second  recess  many  pupils  ate  lunch  at  home  or  school. 
This  recess  probably  increased  the  efficiency  in  the  afternoon 
tests ;  but  as  every  school  has  or  should  have  a  recess  near  this 
period  of  the  school  day,  the  conditions  of  the  Lynchburg  tests 
were  typical,  certainly  for  a  one-session  school  day.  The  de- 

*As  the  Lynchburg  classes  were  slower  in  this  kind  of  work,  twenty-five 
rather  than  twenty  minutes  were  allowed. 


28  STUDIES  OF  MENTAL  FATIGUE 

partmental  system  of  instruction  allowed  no  uniform  program 
of  recitations  and  study  periods  in  the  classes  tested.  The  chil- 
dren represented  for  the  most  part  hygienic  opportunities  at 
home  and  had  been  examined  by  their  teachers  for  eyesight  and 
hearing.  All  the  classes  included  both  boys  and  girls,  the  total 
being  292  boys  and  281  girls.  The  average  age  was  12.55  years. 

The  following  description  is  condensed  and  adapted  from 
the  First  Study,  to  which  the  reader  is  referred  for  further 
discussion.  The  departmental  teacher  put  aside  her  work  for 
my  test,  but  remained  in  the  room  at  my  request.  I  gave 
detailed  directions  to  the  class  and  then  with  the  help  of  the 
teacher  put  on  each  desk  a  test  paper  with  the  blank  side  up. 
After  the  name,  etc.,  had  been  written,  the  children  turned  the 
papers  over  immediately  on  signal  and  worked  steadily  for 
twenty-five  minutes.  Great  care  was  taken  to  be  exact  in  start- 
ing and  stopping.  The  children  thought  they  were  being  exam- 
ined for  correctness  and  speed,  but  did  not  know  how  much  time 
was  being  allowed  and  did  not  rush  toward  the  end.  The  very 
few  children  who  finished  before  the  time  was  out  looked  over 
part  of  their  papers.  The  spirit  of  the  work  was  pleasant  and 
earnest,  and  reduced  to  a  minimum  the  element  of  boredom, 
probably  the  greatest  influence  in  decreasing  the  quantity  and 
quality  of  work  in  the  ordinary  routine  of  the  school  day. 

The  time  schedule  was  so  arranged  as  to  test  each  class  in  the 
morning  and  in  the  afternoon.  The  classes  were  combined  into 
groups  of  two,  one  being  a  half-grade  below  (A)  or  above  (B) 
the  other.  The  first  class  in  a  group  took  the  first  test  in  the 
morning  of  the  first  day  and  the  second  test  in  the  afternoon  of 
the  second  day  following;  the  second  class  took  the  first  test  in 
the  afternoon  of  the  first  day  and  the  second  test  in  the  morning 
of  the  second  day  after.  In  this  way  the  practice  effect  of  the 
first  class  in  the  second  test  in  the  afternoon  was  balanced 
against  that  of  the  second  class  in  the  morning  and  consequently 
neutralized,  leaving  the  fatigue  effect  free  for  comparison  at  the 
two  periods.  This  arrangement  was  based  upon  a  belief  in  the 
approximate  equality  of  the  practice  effect  in  the  two  classes  in 
a  group.  Even  the  slight  differences  that  might  have  occurred 
were  neutralized  by  giving  the  second  test  in  the  morning  to  the 
B  classes  and  in  the  afternoon  to  the  A  classes  of  the  first  four 
groups,  and  then  by  giving  the  second  test  in  the  morning  to  the 
A  classes  and  in  the  afternoon  to  the  B  classes  of  the  second  four 
groups.1 

1One  group  was  composed  of  6A2  and  5B1,  with  the  half-year  relation- 
ship between  classes  as  in  the  other  groups  but  with  different  grades. 


SECOND  STUDY  29 

Two  groups  were  tested  in  a  day,  the  two  classes  of  the  first 
group  at  about  9  :20  A.  M.  and  1 :30  p.  M.,  respectively,  and  the 
two  classes  of  the  second  group  at  about  9  :50  A.  M.  and  2  :00 
p.  M.,  respectively.  On  the  second  day  following,  the  classes 
tested  before  in  the  morning  were  tested  in  the  afternoon,  and 
vice  versa;  but  the  classes  of  the  second  group  followed  as  be- 
fore immediately  after  the  corresponding  classes  of  the  first 
group,  each  group  constituting  a  complete  unit  by  itself  with 
the  same  time  relationship  between  the  classes  as  in  all  the  other 
groups.  Testing  two  groups  a  day  gave  a  wider  representation 
of  the  school  day,  fifty  minutes  of  morning  work  and  fifty  min- 
utes of  afternoon  work. 

The  papers  were  graded  by  me  by  a  gross  method  of  counting- 
answers  only,  very  similar  to  that  used  by  Mr.  Courtis.  Each 
test  contained  thirty-two  points  divided  as  follows :  Two  groups 
of  two  examples  were  each  credited  with  one  point,  this  point 
being  counted  wrong  on  account  of  one  or  more  mistakes  in 
either  example  ;  ten  examples  were  each  credited  with  one  point, 
the  point  being  counted  wrong  on  account  of  one  or  more  mis- 
takes in  the  example ;  ten  examples  were  each  credited  with  two 
points,  one  point  being  counted  wrong  on  account  of  one  mis- 
take, and  two  points  being  counted  wrong  on  account  of  two  or 
more  mistakes,  in  the  example.  A  gross  method  of  counting 
answers  over-emphasizes  mistakes  in  proportion  to  the  total 
amount  of  work  done,  not  only  at  one  period  but  even  in  a  com- 
parison between  the  percentage  of  error  at  two  or  more  periods. 
The  results  of  my  New  York  tests  showed  that  in  the  same 
papers  the  average  increase  in  percentage  of  error  at  the  three 
periods  after  the  first  period  was  by  the  gross  method  3.2659 
times  that  by  the  detailed  method  of  counting  every  figure  put 
down  by  a  child  in  working  the  examples.  The  increase  in  per- 
centage of  error  in  the  present  results  at  the  second  period  is, 
therefore,  greater  than  the  actual  decrease  in  efficiency  of  the 
children  tested.  However,  the  gross  method  takes  far  less  time 
for  grading  papers  and  is  sufficiently  accurate  for  comparison 
of  the  work  at  periods  to  which  it  has  been  uniformly  applied. 


30 


STUDIES  OF  MENTAL  FATIGUE 
Total  Results. 


FIRST   PERIOD 

SECOND   PERIOD 

School 

Class 

Pupils 

Test 

Right 

Wrong 

Test 

Right 

Wronsr 

Biggers           5A 

43 

1 

12.67 

5.02 

2 

16.53 

6.14 

" 

5B 

43 

2 

15.53 

7.42 

1 

12.79 

6.51 

" 

6A 

44 

1 

15.61 

7.34 

2 

16.64 

9.23 

K 

6B 

39 

2 

19.21 

7.10 

1 

18.18 

6.23 

Monroe 

5A 

34 

1 

14.09 

6.44 

2 

15.15 

8.56 

" 

5B 

46 

2 

15.04 

7.26 

1 

10.96 

6.39 

" 

6A 

35 

1 

17.17 

4.54 

2 

20.14 

6.54 

tf 

6B 

32 

2 

21.00 

6.62 

I 

16.59 

5.94 

Federal 

7B 

33 

1 

19.64 

5.00 

2 

21.33 

7.12 

H 

7A 

41 

2 

19.27 

7.12 

1 

16.98 

6.66 

" 

6B 

30 

1 

15.60 

5.27 

2 

17.83 

6.80 

tt 

6A1 

28 

2 

21.86 

7.04 

1 

18.43 

7.54 

(I 

6A2 

33 

1 

14.61 

5.33 

2 

17.09 

6.58 

H 

5B1 

34 

2 

17.24 

7.09 

1 

14.38 

6.41 

" 

5B2 

28 

1 

12.64 

5.96 

2 

15.96 

7.18 

H 

5A 

30 

2 

14.40 

6.37 

1 

11.47 

6.60 

16 

573 

16.60 

6.31 

16.28 

6.90 

Sum  of  right  and  wrong 

points       

22.91 

23.18 

Relative  amount  done.  . 

100.00 

101.18 

Per  cent  right  

72.46 

70.23 

Relative  percent  right.  . 

100.00 

96.92 

The  average  of  right  and  wrong  points  for  the  sixteen  classes 
at  each  period  were  added  and  the  general  average  taken,  in 
which  all  individual,  class,  and  group  variations  were  merged. 
The  sum  of  the  general  average  of  right  and  wrong  points  at  the 
first  period  was  compared  with  that  at  the  second  period,  giving 
an  increase  of  1.18  per  cent  at  the  second  period.  The  per  cent 
right  of  the  sum  of  right  and  wrong  points  at  the  first  period 
was  then  compared  with  the  per  cent  right  at  the  second  period, 
giving  a  decrease  of  3.08  per  cent  at  the  second  period.  The  in- 
crease in  quantity  was  probably  due  in  part  to  the  same  influ- 
ences as  was  the  decrease  in  quality,  greater  speed  and  greater 
carelessness  often  going  together. 

Even  the  slight  decrease  in  efficiency  shown  by  these  results 
is  larger  than  the  actual  decrease  in  the  classes  tested,  because 


SECOND  STUDY  31 

in  Federal  School  the  5A  class  was  somewhat  disturbed  in  its 
afternoon  work  by  the  marching  out  of  the  other  classes,  and 
because  the  7B  and  6B  classes  had  only  a  short  indoor  recess, 
on  account  of  rain,  before  the  afternoon  tests.  This  is  partly 
shown,  though  other  influences  may  have  entered,  by  the  in- 
crease in  quantity  of  2.08  per  cent  and  the  decrease  in  quality 
of  3.37  per  cent  in  the  eight  classes  in  Federal  School,  as  com- 
pared with  the  increase  in  quantity  of  0.22  per  cent  and  the 
decrease  in  quality  of  2.79  per  cent  in  the  eight  classes  in 
Biggers  and  Monroe  Schools. 

As  the  average  per  cent  of  increase  in  quantity  in  the  New 
York  tests,  for  the  three  periods  after  the  first  period,  was  by 
the  detailed  method  of  grading  1.0164  times  that  by  the  gross 
method,  we  can  surmise  that  the  1.18  per  cent  increase  in  quan- 
tity in  the  Lynchburg  tests  by  the  gross  method  would  be  about 
1.20  per  cent  by  the  detailed  method.  And  as  the  average  de- 
crease in  quality  in  the  New  York  tests  was  by  the  detailed 
method  only  0.3062  times  that  by  the  gross  method,  we  can  sur- 
mise that  the  3.08  per  cent  decrease  in  quality  in  the  Lynch- 
burg tests  would  be  about  0.94  per  cent  by  the  detailed  method. 

By  a  comparison  of  the  results  by  the  gross  method  in  the 
twenty-five  minute  test  in  the  afternoon  in  Lynchburg  with  the 
average  of  the  two  ten-minute  tests  in  the  afternoon  in  New 
York,  we  have  1.18  per  cent  increase  in  quantity  in  Lynchburg 
as  compared  with  1.79  per  cent,  and  3.08  per  cent  decrease  in 
quality  as  compared  with  5.61  per  cent.  In  spite  of  the  longer 
requirement  for  continuous  work,  the  Lynchburg  children  show 
a  smaller  decrease  in  efficiency,  probably  on  account  of  their 
better  hygienic  opportunities  at  home. 

In  order  to  determine  whether  the  decrease  in  efficiency  at 
the  second  period  in  Lynchburg  was  less  in  the  more  advanced 
grades,  the  following  percentages  were  calculated:  six  fifth 
grades  (three  groups)  showed  an  increase  in  quantity  of  0.11 
per  cent  and  a  decrease  in  quality  of  2.82  per  cent;  six  sixth 
grades  (three  groups)  showed  an  increase  in  quantity  of  0.36 
per  cent  and  a  decrease  in  quality  of  2.74  per  cent;  two  seventh 
grades  (one  group)  showed  an  increase  in  quantity  of  2.08  per 
cent  and  a  decrease  in  quality  of  3.54  per  cent.  These  slight 
differences  seem  to  have  no  significance,  the  greater  decrease 
in  quality  in  the  seventh  grades  being  due  mainly  to  the  fact 
before  mentioned  that  7B  had  only  a  short  indoor  recess  before 
the  afternoon  test. 


32  STUDIES  OF  MENTAL  FATIGUE 

An  important  consideration  is  the  greater  decrease  in  effi- 
ciency shown  by  the  boys  than  by  the  girls,  this  difference  even 
being  noticeable  in  the  greater  restlessness  of  the  boys  during 
the  tests.  Complete  tables  of  the  sixteen  class  averages  were 
made  of  the  results  by  the  boys  and  the  girls,  and  the  general 
averages,  percentages,  etc.,  were  calculated.  The  boys  showed 
an  increase  in  quantity  of  0.74  per  cent  and  a  decrease  in  qual- 
ity of  4.25  per  cent;  the  girls  showed  an  increase  in  quantity 
of  1.62  per  cent  and  a  decrease  in  quality  of  1.96  per  cent.  The 
boys  showed  an  increase  in  quantity  0.4568  times  that  by  the 
girls  and  a  decrease  in  quality  2.1684  times  that  by  the  girls. 

The  practice  effect  was  calculated  by  rearranging  the  class 
averages  in  columns  according  to  tests  rather  than  periods,  thus 
neutralizing  for  the  most  part  the  decrease  in  efficiency  at  the 
second  period.  The  sixteen  classes  showed  an  increase  in  quan- 
tity of  13.22  per  cent  in  the  second  test  and  a  decrease  in  qual- 
ity of  0.50  per  cent. 


THIRD  STUDY 

The  tests  were  given  in  December,  1914,  to  sixteen  classes, 
476  pupils,  in  the  Intermediate  School  in  Roanoke,  Va.  In 
this  experiment  reasoning  problems  in  arithmetic  were  used  in 
place  of  the  four  fundamental  operations  in  the  New  York  and 
Lynchburg  experiments.  Although  the  continued  alertness  re- 
quired of  grammar-grade  pupils  in  rapid  computation  may  well 
be  considered  indicative  of  hygienic  efficiency  for  other  school 
work,  it  must  be  admitted  that  the  four  fundamental  operations 
may  become  partially  automatic  in  well-drilled  children,  and, 
therefore,  be  less  affected  by  fatigue.  Furthermore,  reasoning 
problems  were  used  in  the  third  experiment  as  involving  pro- 
cesses and  effort  more  generally  needed  in  meeting  school  re- 
quirements. 

In  order  to  carry  out  in  the  third  experiment  the  methods  of 
the  other  two,  it  was  necessary  to  use  two  reasoning  tests  that 
could  be  graded  accurately  and  would  be  approximately  equal 
in  difficulty.  The  tests  selected  were  Forms  1  and  3  of  the 
Courtis  Standard  Test  No.  8,  since  Mr.  Courtis  had  proved  by 
his  very  wide  experience  that  these  tests  were  as  nearly  equal  as 
any  so  far  made.  They  were  given  and  scored  according  to  the 
Courtis  method,  the  number  of  examples  done  and  the  number 
right  being  calculated  from  the  figures  in  the  " Answer"  column. 
The  non-measureable  elements  in  this  gross  method  were  mainly 
neutralized  in  the  comparison  of  morning  and  afternoon  work. 

On  Monday,  December  8,  Form  2  of  Test  No.  8  was  given 
as  a  preliminary  test  to  all  sixteen  classes  in  order  to  acquaint 
them  with  the  matter  and  method  of  the  succeeding  tests ;  but 
the  papers  were  not  scored.  By  trying  ten,  fifteen,  and  twelve 
minutes  as  the  time  limit  for  this  preliminary  test,  the  twelve- 
minute  limit  was  found  to  be  most  suitable  for  the  classes  con- 
cerned. For  the  succeeding  tests  the  classes  were  divided  into 
groups  of  four,  each  group  containing  a  7A,  a  7B,  a  6A,  and  a 
6B  class  of  equal  rank  with  other  classes  of  the  same  half -grade. 
As  the  classes  in  a  group  were  tested  in  rapid  succession,  about 
sixty-five  minutes  were  required  for  a  group — from  9  :25  to 
10:30  in  the  morning  or  from  12:50  to  1:55  in  the  afternoon. 
The  first  test  was  given  to  Group  1  on  Tuesday  morning,  to 
Group  2  on  Tuesday  afternoon,  to  Group  3  011  Wednesday 
morning,  and  to  Group  4  on  Wednesday  afternoon.  The  second 
test  was  given  to  Group  2  on  Thursday  morning,  to  Group  1  011 
Thursday  afternoon,  to  Group  4  on  Friday  morning,  and  to 


34  STUDIES  OF  MENTAL  FATIGUE 

Group  3  on  Friday  afternoon.  Thus  each  class  was  tested  in 
the  morning  and  in  the  afternoon;  and  each  test  was  given  in 
the  morning  and  in  the  afternoon  to  the  same  number  of  classes 
of  relatively  equal  rank.  By  this  method  the  practice  effect  in 
the  second  test  was  neutralized  by  approximately  equal  repre- 
sentation in  the  morning  and  in  the  afternoon  results.  To  com- 
plete this  neutralization  the  classes  in  Groups  1  and  2  were 
tested  in  descending  order  (7 A,  7B,  6 A,  6B),  and  the  classes  in 
Groups  3  and  4  were  tested  in  ascending  order  (6B,  6 A,  7B, 
7A). 

A  teacher  generally  remained  in  the  room  during  a  test,  but 
assisted  me  only  in  distributing  and  collecting  the  papers.  The 
children  enjoyed  the  tests,  which  they  thought  were  only  for 
correctness  and  speed.  They  did  not  know  the  time  limit  for 
the  work ;  and  the  few  that  finished  early  spent  the  extra  time 
in  looking  over  their  papers.  Where  children  were  absent  from 
one  test  or  where  they  did  not  follow  important  directions,  their 
papers  were  thrown  out. 

The  hygienic  conditions  in  the  new  school  building  were  un- 
usually good,  but  there  had  been  no  medical  inspection  of  the 
children.  Opening  exercises  were  held  in  each  room  from  9  :00 
to  9  :20,  recess  was  given  from  12  :15  to  12  :35,  and  the  first  bell 
for  dismissal  was  rung  at  2:15.  The  only  recess  did  not  give 
much  invigoration,  because  the  boys'  playground  was  small  and 
most  girls  remained  indoors  in  spite  of  beautiful  weather. 
Some  pupils  ate  a  light  lunch  at  recess,  but  nearly  all  had  din- 
ner at  home  after  school.  The  departmental  system  of  instruc- 
tion prevailed  throughout  with  half-hour  recitation  periods. 
All  classes  included  both  boys  and  girls,  the  total  represented  in 
my  results  being  212  boys  and  255  girls.  The  average  age  was 
14.18  years. 

After  the  papers  were  scored,  the  averages  of  the  number  of 
examples  done  and  the  number  right  in  the  morning  and  in  the 
afternoon  tests  were  made  for  each  class.  Then  general  aver- 
ages were  made  for  the  sixteen  classes  combined,  and  the  morn- 
ing and  the  afternoon  results  were  compared.  The  number  of 
examples  done  in  the  afternoon  was  0.68  per  cent  greater  than 
in  the  morning;  the  per  cent  of  examples  right  in  the  afternoon 
was  3.22  per  cent  less  than  in  the  morning.  These  per  cents  are 
strikingly  similar  to  those  from  the  Lynchburg  and  New  York 
(average  of  two  afternoon  tests)  experiments,  where  the  in- 
crease in  quantity  in  the  afternoon  was  1.18  and  1.79  per  cent, 
respectively,  and  the  decrease  in  quality  3.08  and  5.61  per  cent, 


TILTED  STUDY 


35 


respectively.     As  was  shown  by  the  New  York  results,  the  de- 
crease in  quality  would  be  less  by  a  detailed  method  of  grading. 

Total  Results. 


Class                Pupils 

Test 

MORNING 

Examples 

Right 

Test 

AFTEENOO 

Examples 

V 

Right 

7A1   26 
7B1   30 

1 

1 

5.96 
5  60 

4.50 
4  20 

2 
2 

6.73 
5.97 

5.27 
4  77 

6A1                     31 

1 

4  87 

3  81 

2 

5  45 

4  23 

6B1    29 

1 

4.83 

3.76 

2 

5.07 

3  97 

7A2   32 

2 

6  84 

5  44 

1 

5  78 

4  00 

7B2                    35 

2 

6  23 

5  09 

1 

5  97 

4  31 

6A2   27 

2 

6  37 

4  81 

1 

5  93 

4  19 

6B2  25 

2 

5  88 

4  56 

1 

4  96 

3  00 

6B3                    24 

1 

4  96 

2  71 

2 

5  33 

3  58 

6A3   26 

1 

5  04 

3  27 

2 

6  42 

4  19 

7B3  35 
7A3                    33 

1 
1 

4.74 
6  64 

3.34 
4  70 

2 
2 

6.06 

7  48 

4.51 

5  27 

6B4  28 

2 

6  00 

4  43 

1 

5  39 

3  54 

6A4  29 
7B4                     28 

2 
2 

5.79 
6  82 

3.83 
4  93 

1 
1 

5.10 
^  Q6 

3.31 

4  00 

7A4   29 

2 

7  00 

5  55 

1 

6  72 

5  14 

16                    467 

5.85 

4.31 

5.89 

4.20 

Relative    number 
done    

100.00 

100  68 

Per  cent  right  
Relative  per  cent 
right 

73.68 
100  00 

71.31 

Qft  78 

The  practice  effect  was  calculated  by  rearranging  the  class 
averages  according  to  first  or  second  test  rather  than  according 
to  morning  and  afternoon,  thus  neutralizing  for  the  most  part 
the  decrease  in  efficiency  in  the  afternoon.  The  sixteen  classes 
showed  in  the  second  test  an  average  increase  of  12.43  per  cent 
in  quantity  and  an  average  increase  of  7.16  per  cent  in  quality. 
This  large  practice  effect  was  mainly  due  to  the  difficulty  the 
children  had  at  first  in  disregarding  unnecessary  figures  in  some 
of  the  examples. 

The  seventh  grade  showed  more  relative  efficiency  in  the  aft- 
ernoon than  did  the  sixth  grade,  probably  on  account  of  better 
discipline  in  the  former.  The  seventh  grade  had  an  increase  of 
1.61  per  cent  in  quantity  in  the  afternoon  and  a  decrease  of  2.82 
per  cent  in  quality ;  the  sixth  grade  had  a  decrease  of  0.04  per 
cent  in  quantity  and  a  decrease  of  3.67  per  cent  in  quality. 


36  STUDIES  OF  MENTAL  FATIGUE 

Complete  tables  of  class  and  general  averages  were  made  for 
the  girls  and  for  the  boys,  showing  the  greater  relative  efficiency 
of  the  former  in  the  afternoon.  The  girls  had  an  increase  of 
1.78  per  cent  in  quantity  in  the  afternoon  and  a  decrease  of  2.48 
per  cent  in  quality;  the  boys  a  decrease  of  1.30  per  cent  in 
quantity  and  a  decrease  of  3.76  per  cent  in  quality.  These 
significant  results  are  similar  to  those  from  the  Lynchburg  tests. 


CONCLUSIONS 

The  most  important  features  of  these  experiments  were  the 
giving  (a)  of  actual  school  tests  (b)  under  actual  school  condi- 
tions (c)  by  the  same  examiner  with  the  same  methods  (d)  to  a 
large  number  of  classes  and  pupils.  Every  possible  effort  was 
made  to  get  the  work  and  attitude  of  the  routine  school  day  and 
to  eliminate  individual  and  group  variations.  The  comparison 
of  morning  and  afternoon  results  probably  neutralized  the  effect 
of  two  differences  from  routine  conditions :  the  tests  were  given 
by  an  outsider  and  offered  a  break  in  the  regular  school  re- 
quirements. 

The  per  cent  of  increase  in  quantity  and  of  decrease  in  qual- 
ity in  the  afternoon  results,  as  compared  with  the  morning  re- 
sults, by  the  gross  method  of  grading,  may  be  summarized  as 
follows : 


City 

Classes 

Pupils 

Increase  in 
Quantity 

Decrease  in 
Quality 

New  York1 

40 

1,153 

1.79 

5.61 

L/ynchburg 

16 

573 

1.18 

3.08 

Roanoke   

16 

476 

0.68 

3.22 

2,202 


1.22 


3.97 


Seventy-two  classes,  2,202  children,  in  three  cities,  showed  in 
the  afternoon  results  an  average  increase  in  quantity  of  1.22  per 
cent  and  an  average  decrease  in  quality  of  3.97  per  cent. 


The  following  tentative  conclusions  seem  justified  for  gram- 
mar-grade pupils  :2 

1.  Mental  fatigue  in  relation  to  the  daily  school  program  is 
far  less  than  is  generally  believed,  even  if  the  tendency  to  do  a 
greater  amount  of  work  with  a  greater  per  cent  of  error  can  be 
partly  attributed  to  fatigue. 


irrhe  averages  of  the  two  afternoon  tests  in  New  York  are  compared  with 
the  first  morning  test,  as  the  second  morning  test  did  not  represent  the 
time  or  freshness  of  the  morning  test  in  Lynchburg  and  Roanoke,  and  the 
results  were  even  below  the  afternoon  average. 

2These  conclusions  will  probably  not  apply  to  primary  grades  (to  most 
children  under  eleven  years  of  age),  without  modification  as  to  length  of 
daily  school  program,  etc. 


38  STUDIES  OF  MENTAL  FATIGUE 

2.  The  opinion  regarding  the  graduated  advantages  of  suc- 
cessive periods  of  the  school  day,  and  the  sentiment  in  favor  of 
putting  arithmetic  and  other  supposedly  difficult  subjects  near 
the  opening  of  the  morning  and  afternoon  sessions,  with  an  em- 
phasis upon  the  morning  session,  have  not  a  sufficiently  proved 
basis. 

3.  The  decrease  in  quality  of  work  by  pupils  as  the  day  ad- 
vances, considered  to  be  more  or  less  general   in  schools,   is 
mainly  due  (a)  to  improper  ventilation,  lighting,  heating,  seat- 
ing, etc.,  (b)  to  physical  defects  in  the  children,  and  (c)  to  loss 
of   interest  by   pupil   and   teacher   in   the  monotonous   school 
routine. 

4.  With  sound  bodies,  a  hygienic  school,  proper  classifica- 
tion, a  vital  and  varied  curriculum,   and  live  teachers,  most 
grammar-grade  pupils  will  present  no  problem  of  fatigue  in  re- 
lation to  the  daily  school  program. 


VITA. 

WILLIAM  HARRY  HECK:  Born  Raleigh,  N.  C.,  1879;  B.  A., 
Wake  Forest  College,  N.  C.,  1897;  Assistant  Principal,  Raleigh 
Male  Academy,  1897-98 ;  M.  A.,  Wake  Forest  College,  1899 ; 
Graduate  Student,  Columbia  University,  1899-1902;  Univer- 
sity Fellow,  1900-01;  Honorary  Fellow,  1901-02;  Assistant 
Secretary,  General  Education  Board,  1902-05 ;  Professor  of 
Education,  University  of  Virginia,  1905 — ;  Graduate  Student, 
Columbia  University,  1911-12. 


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